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Abstract

The level set technique is an implicit shape-based image reconstruction method that allows the recovery of the location, size and shape of objects of distinct contrast with well-defined boundaries embedded in a medium of homogeneous or moderately varying background parameters. In the case of diffuse optical tomography, level sets can be employed to simultaneously recover inclusions that differ in their absorption or scattering parameters from the background medium. This paper applies the level set method to the three-dimensional reconstruction of objects from simulated model data and from experimental frequency-domain data of light transmission obtained from a cylindrical phantom with tissue-like parameters. The shape and contrast of two inclusions, differing in absorption and diffusion parameters from the background, respectively, are reconstructed simultaneously. We compare the performance of level set reconstruction with results from an image-based method using a Gauss-Newton iterative approach, and show that the level set technique can improve the detection and localisation of small, high-contrast targets.

Figures (12)

Fig. 1. Object geometry for simulated model data, and phantom for experimental data. The object is a cylinder with embedded cylindrical targets in the central plane. Source and detector locations on the surface are marked with ‘x’ and ‘o’, respectively (a). Cross sections in the central xy plane show the position of the absorption (b) and diffusion target (c).

Fig. 3. Cross sections through mean and variance images of shape-only level set reconstructions of absorption and scattering from 50 background noise realisations. Rows from top to bottom: absorption mean, absorption variance, diffusion mean and diffusion variance. In each row, images from left to right are for background variation levels of 0, 10, 20 and 50% Media 1.

Fig. 4. Cross sections through the absorption (left) and diffusion (right) target distributions (dashed line) and level set shape reconstructions for one sample of each of the background variation levels. Note that the lines for 0, 10 and 20% background variation overlap.

Fig. 5. Level set shape errors ε for absorption (blue) and diffusion images (red) as a function of background noise level. Plotted are the results for both the shape-only (solid lines) and combined shape and contrast reconstructions (dashed lines).

Fig. 6. Cross sections through mean and variance images of combined shape and contrast level set reconstructions of absorption and scattering from 50 background noise realisations. Rows from top to bottom: absorption mean, absorption variance, diffusion mean and diffusion variance. In each row, images from left to right correspond to background variation levels of 0%, 10%, 20% and 50% (Media 2).

Fig. 7. Evolution of absorption parameter x1,i(n) (left) and diffusion parameter x2,i(n) (right) as a function of iteration number corresponding to the two difference reconstruction problems in Fig. 6. Target values are plotted as dashed lines.

Fig. 8. Cross sections through the absorption (left) and diffusion (right) target distributions (dashed line) and level set shape+contrast difference reconstructions for one sample of each of the background variation levels.

Fig. 9. Cross sections for Gauss-Newton-Krylov image-based difference reconstructions. Top row: absorption, second row: diffusion images. Columns from left to right are reconstructions of data from the four background realisations shown in Fig. 2.